package skiplists.lockfree;

/*
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Sun designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Sun in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
 * CA 95054 USA or visit www.sun.com if you need additional information or
 * have any questions.
 */

/*
 * This file is available under and governed by the GNU General Public
 * License version 2 only, as published by the Free Software Foundation.
 * However, the following notice accompanied the original version of this
 * file:
 *
 * Written by Doug Lea with assistance from members of JCP JSR-166
 * Expert Group and released to the public domain, as explained at
 * http://creativecommons.org/licenses/publicdomain
 */

import java.util.AbstractCollection;
import java.util.AbstractMap;
import java.util.AbstractSet;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.ConcurrentModificationException;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.NavigableSet;
import java.util.NoSuchElementException;
import java.util.Random;
import java.util.Set;
import java.util.SortedMap;
import java.util.concurrent.ConcurrentNavigableMap;
import java.util.concurrent.ConcurrentSkipListSet;
import java.util.concurrent.atomic.AtomicReferenceFieldUpdater;

import contention.abstractions.CompositionalMap;
import contention.abstractions.CompositionalMap.Vars;

/**
 * A scalable concurrent {@link ConcurrentNavigableMap} implementation. The map
 * is sorted according to the {@linkplain Comparable natural ordering} of its
 * keys, or by a {@link Comparator} provided at map creation time, depending on
 * which constructor is used.
 * 
 * <p>
 * This class implements a concurrent variant of <a
 * href="http://www.cs.umd.edu/~pugh/">SkipLists</a> providing expected average
 * <i>log(n)</i> time cost for the <tt>containsKey</tt>, <tt>get</tt>,
 * <tt>put</tt> and <tt>remove</tt> operations and their variants. Insertion,
 * removal, update, and access operations safely execute concurrently by
 * multiple threads. Iterators are <i>weakly consistent</i>, returning elements
 * reflecting the state of the map at some point at or since the creation of the
 * iterator. They do <em>not</em> throw {@link ConcurrentModificationException},
 * and may proceed concurrently with other operations. Ascending key ordered
 * views and their iterators are faster than descending ones.
 * 
 * <p>
 * All <tt>Map.Entry</tt> pairs returned by methods in this class and its views
 * represent snapshots of mappings at the time they were produced. They do
 * <em>not</em> support the <tt>Entry.setValue</tt> method. (Note however that
 * it is possible to change mappings in the associated map using <tt>put</tt>,
 * <tt>putIfAbsent</tt>, or <tt>replace</tt>, depending on exactly which effect
 * you need.)
 * 
 * <p>
 * Beware that, unlike in most collections, the <tt>size</tt> method is
 * <em>not</em> a constant-time operation. Because of the asynchronous nature of
 * these maps, determining the current number of elements requires a traversal
 * of the elements. Additionally, the bulk operations <tt>putAll</tt>,
 * <tt>equals</tt>, and <tt>clear</tt> are <em>not</em> guaranteed to be
 * performed atomically. For example, an iterator operating concurrently with a
 * <tt>putAll</tt> operation might view only some of the added elements.
 * 
 * <p>
 * This class and its views and iterators implement all of the <em>optional</em>
 * methods of the {@link Map} and {@link Iterator} interfaces. Like most other
 * concurrent collections, this class does <em>not</em> permit the use of
 * <tt>null</tt> keys or values because some null return values cannot be
 * reliably distinguished from the absence of elements.
 * 
 * <p>
 * This class is a member of the <a href="{@docRoot}
 * /../technotes/guides/collections/index.html"> Java Collections Framework</a>.
 * 
 * @author Doug Lea
 * @param <K>
 *            the type of keys maintained by this map
 * @param <V>
 *            the type of mapped values
 * @since 1.6
 */
public class NonBlockingJavaSkipListMap<K, V> extends AbstractMap<K, V>
		implements ConcurrentNavigableMap<K, V>, CompositionalMap<K, V>,
		Cloneable, java.io.Serializable {
	/*
	 * This class implements a tree-like two-dimensionally linked skip list in
	 * which the index levels are represented in separate nodes from the base
	 * nodes holding data. There are two reasons for taking this approach
	 * instead of the usual array-based structure: 1) Array based
	 * implementations seem to encounter more complexity and overhead 2) We can
	 * use cheaper algorithms for the heavily-traversed index lists than can be
	 * used for the base lists. Here's a picture of some of the basics for a
	 * possible list with 2 levels of index:
	 * 
	 * Head nodes Index nodes +-+ right +-+ +-+ |2|---------------->|
	 * |--------------------->| |->null +-+ +-+ +-+ | down | | v v v +-+ +-+ +-+
	 * +-+ +-+ +-+ |1|----------->| |->| |------>| |----------->| |------>|
	 * |->null +-+ +-+ +-+ +-+ +-+ +-+ v | | | | | Nodes next v v v v v +-+ +-+
	 * +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ |
	 * |->|A|->|B|->|C|->|D|->|E|->|F|->|G|->|H|->|I|->|J|->|K|->null +-+ +-+
	 * +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+
	 * 
	 * The base lists use a variant of the HM linked ordered set algorithm. See
	 * Tim Harris, "A pragmatic implementation of non-blocking linked lists"
	 * http://www.cl.cam.ac.uk/~tlh20/publications.html and Maged Michael "High
	 * Performance Dynamic Lock-Free Hash Tables and List-Based Sets"
	 * http://www.research.ibm.com/people/m/michael/pubs.htm. The basic idea in
	 * these lists is to mark the "next" pointers of deleted nodes when deleting
	 * to avoid conflicts with concurrent insertions, and when traversing to
	 * keep track of triples (predecessor, node, successor) in order to detect
	 * when and how to unlink these deleted nodes.
	 * 
	 * Rather than using mark-bits to mark list deletions (which can be slow and
	 * space-intensive using AtomicMarkedReference), nodes use direct CAS'able
	 * next pointers. On deletion, instead of marking a pointer, they splice in
	 * another node that can be thought of as standing for a marked pointer
	 * (indicating this by using otherwise impossible field values). Using plain
	 * nodes acts roughly like "boxed" implementations of marked pointers, but
	 * uses new nodes only when nodes are deleted, not for every link. This
	 * requires less space and supports faster traversal. Even if marked
	 * references were better supported by JVMs, traversal using this technique
	 * might still be faster because any search need only read ahead one more
	 * node than otherwise required (to check for trailing marker) rather than
	 * unmasking mark bits or whatever on each read.
	 * 
	 * This approach maintains the essential property needed in the HM algorithm
	 * of changing the next-pointer of a deleted node so that any other CAS of
	 * it will fail, but implements the idea by changing the pointer to point to
	 * a different node, not by marking it. While it would be possible to
	 * further squeeze space by defining marker nodes not to have key/value
	 * fields, it isn't worth the extra type-testing overhead. The deletion
	 * markers are rarely encountered during traversal and are normally quickly
	 * garbage collected. (Note that this technique would not work well in
	 * systems without garbage collection.)
	 * 
	 * In addition to using deletion markers, the lists also use nullness of
	 * value fields to indicate deletion, in a style similar to typical
	 * lazy-deletion schemes. If a node's value is null, then it is considered
	 * logically deleted and ignored even though it is still reachable. This
	 * maintains proper control of concurrent replace vs delete operations -- an
	 * attempted replace must fail if a delete beat it by nulling field, and a
	 * delete must return the last non-null value held in the field. (Note:
	 * Null, rather than some special marker, is used for value fields here
	 * because it just so happens to mesh with the Map API requirement that
	 * method get returns null if there is no mapping, which allows nodes to
	 * remain concurrently readable even when deleted. Using any other marker
	 * value here would be messy at best.)
	 * 
	 * Here's the sequence of events for a deletion of node n with predecessor b
	 * and successor f, initially:
	 * 
	 * +------+ +------+ +------+ ... | b |------>| n |----->| f | ... +------+
	 * +------+ +------+
	 * 
	 * 1. CAS n's value field from non-null to null. From this point on, no
	 * public operations encountering the node consider this mapping to exist.
	 * However, other ongoing insertions and deletions might still modify n's
	 * next pointer.
	 * 
	 * 2. CAS n's next pointer to point to a new marker node. From this point
	 * on, no other nodes can be appended to n. which avoids deletion errors in
	 * CAS-based linked lists.
	 * 
	 * +------+ +------+ +------+ +------+ ... | b |------>| n
	 * |----->|marker|------>| f | ... +------+ +------+ +------+ +------+
	 * 
	 * 3. CAS b's next pointer over both n and its marker. From this point on,
	 * no new traversals will encounter n, and it can eventually be GCed.
	 * +------+ +------+ ... | b |----------------------------------->| f | ...
	 * +------+ +------+
	 * 
	 * A failure at step 1 leads to simple retry due to a lost race with another
	 * operation. Steps 2-3 can fail because some other thread noticed during a
	 * traversal a node with null value and helped out by marking and/or
	 * unlinking. This helping-out ensures that no thread can become stuck
	 * waiting for progress of the deleting thread. The use of marker nodes
	 * slightly complicates helping-out code because traversals must track
	 * consistent reads of up to four nodes (b, n, marker, f), not just (b, n,
	 * f), although the next field of a marker is immutable, and once a next
	 * field is CAS'ed to point to a marker, it never again changes, so this
	 * requires less care.
	 * 
	 * Skip lists add indexing to this scheme, so that the base-level traversals
	 * start close to the locations being found, inserted or deleted -- usually
	 * base level traversals only traverse a few nodes. This doesn't change the
	 * basic algorithm except for the need to make sure base traversals start at
	 * predecessors (here, b) that are not (structurally) deleted, otherwise
	 * retrying after processing the deletion.
	 * 
	 * Index levels are maintained as lists with volatile next fields, using CAS
	 * to link and unlink. Races are allowed in index-list operations that can
	 * (rarely) fail to link in a new index node or delete one. (We can't do
	 * this of course for data nodes.) However, even when this happens, the
	 * index lists remain sorted, so correctly serve as indices. This can impact
	 * performance, but since skip lists are probabilistic anyway, the net
	 * result is that under contention, the effective "p" value may be lower
	 * than its nominal value. And race windows are kept small enough that in
	 * practice these failures are rare, even under a lot of contention.
	 * 
	 * The fact that retries (for both base and index lists) are relatively
	 * cheap due to indexing allows some minor simplifications of retry logic.
	 * Traversal restarts are performed after most "helping-out" CASes. This
	 * isn't always strictly necessary, but the implicit backoffs tend to help
	 * reduce other downstream failed CAS's enough to outweigh restart cost.
	 * This worsens the worst case, but seems to improve even highly contended
	 * cases.
	 * 
	 * Unlike most skip-list implementations, index insertion and deletion here
	 * require a separate traversal pass occuring after the base-level action,
	 * to add or remove index nodes. This adds to single-threaded overhead, but
	 * improves contended multithreaded performance by narrowing interference
	 * windows, and allows deletion to ensure that all index nodes will be made
	 * unreachable upon return from a public remove operation, thus avoiding
	 * unwanted garbage retention. This is more important here than in some
	 * other data structures because we cannot null out node fields referencing
	 * user keys since they might still be read by other ongoing traversals.
	 * 
	 * Indexing uses skip list parameters that maintain good search performance
	 * while using sparser-than-usual indices: The hardwired parameters k=1,
	 * p=0.5 (see method randomLevel) mean that about one-quarter of the nodes
	 * have indices. Of those that do, half have one level, a quarter have two,
	 * and so on (see Pugh's Skip List Cookbook, sec 3.4). The expected total
	 * space requirement for a map is slightly less than for the current
	 * implementation of java.util.TreeMap.
	 * 
	 * Changing the level of the index (i.e, the height of the tree-like
	 * structure) also uses CAS. The head index has initial level/height of one.
	 * Creation of an index with height greater than the current level adds a
	 * level to the head index by CAS'ing on a new top-most head. To maintain
	 * good performance after a lot of removals, deletion methods heuristically
	 * try to reduce the height if the topmost levels appear to be empty. This
	 * may encounter races in which it possible (but rare) to reduce and "lose"
	 * a level just as it is about to contain an index (that will then never be
	 * encountered). This does no structural harm, and in practice appears to be
	 * a better option than allowing unrestrained growth of levels.
	 * 
	 * The code for all this is more verbose than you'd like. Most operations
	 * entail locating an element (or position to insert an element). The code
	 * to do this can't be nicely factored out because subsequent uses require a
	 * snapshot of predecessor and/or successor and/or value fields which can't
	 * be returned all at once, at least not without creating yet another object
	 * to hold them -- creating such little objects is an especially bad idea
	 * for basic internal search operations because it adds to GC overhead.
	 * (This is one of the few times I've wished Java had macros.) Instead, some
	 * traversal code is interleaved within insertion and removal operations.
	 * The control logic to handle all the retry conditions is sometimes twisty.
	 * Most search is broken into 2 parts. findPredecessor() searches index
	 * nodes only, returning a base-level predecessor of the key. findNode()
	 * finishes out the base-level search. Even with this factoring, there is a
	 * fair amount of near-duplication of code to handle variants.
	 * 
	 * For explanation of algorithms sharing at least a couple of features with
	 * this one, see Mikhail Fomitchev's thesis
	 * (http://www.cs.yorku.ca/~mikhail/), Keir Fraser's thesis
	 * (http://www.cl.cam.ac.uk/users/kaf24/), and Hakan Sundell's thesis
	 * (http://www.cs.chalmers.se/~phs/).
	 * 
	 * Given the use of tree-like index nodes, you might wonder why this doesn't
	 * use some kind of search tree instead, which would support somewhat faster
	 * search operations. The reason is that there are no known efficient
	 * lock-free insertion and deletion algorithms for search trees. The
	 * immutability of the "down" links of index nodes (as opposed to mutable
	 * "left" fields in true trees) makes this tractable using only CAS
	 * operations.
	 * 
	 * Notation guide for local variables Node: b, n, f for predecessor, node,
	 * successor Index: q, r, d for index node, right, down. t for another index
	 * node Head: h Levels: j Keys: k, key Values: v, value Comparisons: c
	 */

	private static final long serialVersionUID = -8627078645895051609L;

	/**
	 * Generates the initial random seed for the cheaper per-instance random
	 * number generators used in randomLevel.
	 */
	private static final Random seedGenerator = new Random();

	/**
	 * Special value used to identify base-level header
	 */
	private static final Object BASE_HEADER = new Object();

	/**
	 * The topmost head index of the skiplist.
	 */
	private transient volatile HeadIndex<K, V> head;

	/**
	 * The comparator used to maintain order in this map, or null if using
	 * natural ordering.
	 * 
	 * @serial
	 */
	private final Comparator<? super K> comparator;

	/**
	 * Seed for simple random number generator. Not volatile since it doesn't
	 * matter too much if different threads don't see updates.
	 */
	private transient int randomSeed;

	/** Lazily initialized key set */
	private transient KeySet keySet;
	/** Lazily initialized entry set */
	private transient EntrySet entrySet;
	/** Lazily initialized values collection */
	private transient Values values;
	/** Lazily initialized descending key set */
	private transient ConcurrentNavigableMap<K, V> descendingMap;

	/**
	 * Initializes or resets state. Needed by constructors, clone, clear,
	 * readObject. and ConcurrentSkipListSet.clone. (Note that comparator must
	 * be separately initialized.)
	 */
	final void initialize() {
		keySet = null;
		entrySet = null;
		values = null;
		descendingMap = null;
		randomSeed = seedGenerator.nextInt() | 0x0100; // ensure nonzero
		head = new HeadIndex<K, V>(new Node<K, V>(null, BASE_HEADER, null),
				null, null, 1);
	}

	/** Updater for casHead */
	private static final AtomicReferenceFieldUpdater<NonBlockingJavaSkipListMap, HeadIndex> headUpdater = AtomicReferenceFieldUpdater
			.newUpdater(NonBlockingJavaSkipListMap.class, HeadIndex.class,
					"head");

	/**
	 * compareAndSet head node
	 */
	private boolean casHead(HeadIndex<K, V> cmp, HeadIndex<K, V> val) {
		return headUpdater.compareAndSet(this, cmp, val);
	}

	/* ---------------- Nodes -------------- */

	/**
	 * Nodes hold keys and values, and are singly linked in sorted order,
	 * possibly with some intervening marker nodes. The list is headed by a
	 * dummy node accessible as head.node. The value field is declared only as
	 * Object because it takes special non-V values for marker and header nodes.
	 */
	static final class Node<K, V> {
		final K key;
		volatile Object value;
		volatile Node<K, V> next;

		/**
		 * Creates a new regular node.
		 */
		Node(K key, Object value, Node<K, V> next) {
			this.key = key;
			this.value = value;
			this.next = next;
		}

		/**
		 * Creates a new marker node. A marker is distinguished by having its
		 * value field point to itself. Marker nodes also have null keys, a fact
		 * that is exploited in a few places, but this doesn't distinguish
		 * markers from the base-level header node (head.node), which also has a
		 * null key.
		 */
		Node(Node<K, V> next) {
			this.key = null;
			this.value = this;
			this.next = next;
		}

		/** Updater for casNext */
		static final AtomicReferenceFieldUpdater<Node, Node> nextUpdater = AtomicReferenceFieldUpdater
				.newUpdater(Node.class, Node.class, "next");

		/** Updater for casValue */
		static final AtomicReferenceFieldUpdater<Node, Object> valueUpdater = AtomicReferenceFieldUpdater
				.newUpdater(Node.class, Object.class, "value");

		/**
		 * compareAndSet value field
		 */
		boolean casValue(Object cmp, Object val) {
			return valueUpdater.compareAndSet(this, cmp, val);
		}

		/**
		 * compareAndSet next field
		 */
		boolean casNext(Node<K, V> cmp, Node<K, V> val) {
			return nextUpdater.compareAndSet(this, cmp, val);
		}

		/**
		 * Returns true if this node is a marker. This method isn't actually
		 * called in any current code checking for markers because callers will
		 * have already read value field and need to use that read (not another
		 * done here) and so directly test if value points to node.
		 * 
		 * @param n
		 *            a possibly null reference to a node
		 * @return true if this node is a marker node
		 */
		boolean isMarker() {
			return value == this;
		}

		/**
		 * Returns true if this node is the header of base-level list.
		 * 
		 * @return true if this node is header node
		 */
		boolean isBaseHeader() {
			return value == BASE_HEADER;
		}

		/**
		 * Tries to append a deletion marker to this node.
		 * 
		 * @param f
		 *            the assumed current successor of this node
		 * @return true if successful
		 */
		boolean appendMarker(Node<K, V> f) {
			return casNext(f, new Node<K, V>(f));
		}

		/**
		 * Helps out a deletion by appending marker or unlinking from
		 * predecessor. This is called during traversals when value field seen
		 * to be null.
		 * 
		 * @param b
		 *            predecessor
		 * @param f
		 *            successor
		 */
		void helpDelete(Node<K, V> b, Node<K, V> f) {
			/*
			 * Rechecking links and then doing only one of the help-out stages
			 * per call tends to minimize CAS interference among helping
			 * threads.
			 */
			if (f == next && this == b.next) {
				if (f == null || f.value != f) // not already marked
					appendMarker(f);
				else
					b.casNext(this, f.next);
			}
		}

		/**
		 * Returns value if this node contains a valid key-value pair, else
		 * null.
		 * 
		 * @return this node's value if it isn't a marker or header or is
		 *         deleted, else null.
		 */
		V getValidValue() {
			Object v = value;
			if (v == this || v == BASE_HEADER)
				return null;
			return (V) v;
		}

		/**
		 * Creates and returns a new SimpleImmutableEntry holding current
		 * mapping if this node holds a valid value, else null.
		 * 
		 * @return new entry or null
		 */
		AbstractMap.SimpleImmutableEntry<K, V> createSnapshot() {
			V v = getValidValue();
			if (v == null)
				return null;
			return new AbstractMap.SimpleImmutableEntry<K, V>(key, v);
		}
	}

	/* ---------------- Indexing -------------- */

	/**
	 * Index nodes represent the levels of the skip list. Note that even though
	 * both Nodes and Indexes have forward-pointing fields, they have different
	 * types and are handled in different ways, that can't nicely be captured by
	 * placing field in a shared abstract class.
	 */
	static class Index<K, V> {
		final Node<K, V> node;
		final Index<K, V> down;
		volatile Index<K, V> right;

		/**
		 * Creates index node with given values.
		 */
		Index(Node<K, V> node, Index<K, V> down, Index<K, V> right) {
			this.node = node;
			this.down = down;
			this.right = right;
		}

		/** Updater for casRight */
		static final AtomicReferenceFieldUpdater<Index, Index> rightUpdater = AtomicReferenceFieldUpdater
				.newUpdater(Index.class, Index.class, "right");

		/**
		 * compareAndSet right field
		 */
		final boolean casRight(Index<K, V> cmp, Index<K, V> val) {
			return rightUpdater.compareAndSet(this, cmp, val);
		}

		/**
		 * Returns true if the node this indexes has been deleted.
		 * 
		 * @return true if indexed node is known to be deleted
		 */
		final boolean indexesDeletedNode() {
			return node.value == null;
		}

		/**
		 * Tries to CAS newSucc as successor. To minimize races with unlink that
		 * may lose this index node, if the node being indexed is known to be
		 * deleted, it doesn't try to link in.
		 * 
		 * @param succ
		 *            the expected current successor
		 * @param newSucc
		 *            the new successor
		 * @return true if successful
		 */
		final boolean link(Index<K, V> succ, Index<K, V> newSucc) {
			Node<K, V> n = node;
			newSucc.right = succ;
			return n.value != null && casRight(succ, newSucc);
		}

		/**
		 * Tries to CAS right field to skip over apparent successor succ. Fails
		 * (forcing a retraversal by caller) if this node is known to be
		 * deleted.
		 * 
		 * @param succ
		 *            the expected current successor
		 * @return true if successful
		 */
		final boolean unlink(Index<K, V> succ) {
			// if(STRUCT_MODS)
			// counts.get().structMods++;
			return !indexesDeletedNode() && casRight(succ, succ.right);
		}
	}

	/* ---------------- Head nodes -------------- */

	/**
	 * Nodes heading each level keep track of their level.
	 */
	static final class HeadIndex<K, V> extends Index<K, V> {
		final int level;

		HeadIndex(Node<K, V> node, Index<K, V> down, Index<K, V> right,
				int level) {
			super(node, down, right);
			this.level = level;
		}
	}

	/* ---------------- Comparison utilities -------------- */

	/**
	 * Represents a key with a comparator as a Comparable.
	 * 
	 * Because most sorted collections seem to use natural ordering on
	 * Comparables (Strings, Integers, etc), most internal methods are geared to
	 * use them. This is generally faster than checking per-comparison whether
	 * to use comparator or comparable because it doesn't require a (Comparable)
	 * cast for each comparison. (Optimizers can only sometimes remove such
	 * redundant checks themselves.) When Comparators are used,
	 * ComparableUsingComparators are created so that they act in the same way
	 * as natural orderings. This penalizes use of Comparators vs Comparables,
	 * which seems like the right tradeoff.
	 */
	static final class ComparableUsingComparator<K> implements Comparable<K> {
		final K actualKey;
		final Comparator<? super K> cmp;

		ComparableUsingComparator(K key, Comparator<? super K> cmp) {
			this.actualKey = key;
			this.cmp = cmp;
		}

		public int compareTo(K k2) {
			return cmp.compare(actualKey, k2);
		}
	}

	/**
	 * If using comparator, return a ComparableUsingComparator, else cast key as
	 * Comparable, which may cause ClassCastException, which is propagated back
	 * to caller.
	 */
	private Comparable<? super K> comparable(Object key)
			throws ClassCastException {
		if (key == null)
			throw new NullPointerException();
		if (comparator != null)
			return new ComparableUsingComparator<K>((K) key, comparator);
		else
			return (Comparable<? super K>) key;
	}

	/**
	 * Compares using comparator or natural ordering. Used when the
	 * ComparableUsingComparator approach doesn't apply.
	 */
	int compare(K k1, K k2) throws ClassCastException {
		Comparator<? super K> cmp = comparator;
		if (cmp != null)
			return cmp.compare(k1, k2);
		else
			return ((Comparable<? super K>) k1).compareTo(k2);
	}

	/**
	 * Returns true if given key greater than or equal to least and strictly
	 * less than fence, bypassing either test if least or fence are null. Needed
	 * mainly in submap operations.
	 */
	boolean inHalfOpenRange(K key, K least, K fence) {
		if (key == null)
			throw new NullPointerException();
		return ((least == null || compare(key, least) >= 0) && (fence == null || compare(
				key, fence) < 0));
	}

	/**
	 * Returns true if given key greater than or equal to least and less or
	 * equal to fence. Needed mainly in submap operations.
	 */
	boolean inOpenRange(K key, K least, K fence) {
		if (key == null)
			throw new NullPointerException();
		return ((least == null || compare(key, least) >= 0) && (fence == null || compare(
				key, fence) <= 0));
	}

	/* ---------------- Traversal -------------- */

	/**
	 * Returns a base-level node with key strictly less than given key, or the
	 * base-level header if there is no such node. Also unlinks indexes to
	 * deleted nodes found along the way. Callers rely on this side-effect of
	 * clearing indices to deleted nodes.
	 * 
	 * @param key
	 *            the key
	 * @return a predecessor of key
	 */
	private Node<K, V> findPredecessor(Comparable<? super K> key) {
		if (key == null)
			throw new NullPointerException(); // don't postpone errors
		for (;;) {
			Index<K, V> q = head;
			Index<K, V> r = q.right;
			for (;;) {
				if (r != null) {
					Node<K, V> n = r.node;
					K k = n.key;
					if (n.value == null) {
						if (!q.unlink(r))
							break; // restart
						r = q.right; // reread r
						continue;
					}
					if (key.compareTo(k) > 0) {
						q = r;
						r = r.right;
						continue;
					}
				}
				Index<K, V> d = q.down;
				if (d != null) {
					q = d;
					r = d.right;
				} else
					return q.node;
			}
		}
	}

	/**
	 * Returns node holding key or null if no such, clearing out any deleted
	 * nodes seen along the way. Repeatedly traverses at base-level looking for
	 * key starting at predecessor returned from findPredecessor, processing
	 * base-level deletions as encountered. Some callers rely on this
	 * side-effect of clearing deleted nodes.
	 * 
	 * Restarts occur, at traversal step centered on node n, if:
	 * 
	 * (1) After reading n's next field, n is no longer assumed predecessor b's
	 * current successor, which means that we don't have a consistent 3-node
	 * snapshot and so cannot unlink any subsequent deleted nodes encountered.
	 * 
	 * (2) n's value field is null, indicating n is deleted, in which case we
	 * help out an ongoing structural deletion before retrying. Even though
	 * there are cases where such unlinking doesn't require restart, they aren't
	 * sorted out here because doing so would not usually outweigh cost of
	 * restarting.
	 * 
	 * (3) n is a marker or n's predecessor's value field is null, indicating
	 * (among other possibilities) that findPredecessor returned a deleted node.
	 * We can't unlink the node because we don't know its predecessor, so rely
	 * on another call to findPredecessor to notice and return some earlier
	 * predecessor, which it will do. This check is only strictly needed at
	 * beginning of loop, (and the b.value check isn't strictly needed at all)
	 * but is done each iteration to help avoid contention with other threads by
	 * callers that will fail to be able to change links, and so will retry
	 * anyway.
	 * 
	 * The traversal loops in doPut, doRemove, and findNear all include the same
	 * three kinds of checks. And specialized versions appear in findFirst, and
	 * findLast and their variants. They can't easily share code because each
	 * uses the reads of fields held in locals occurring in the orders they were
	 * performed.
	 * 
	 * @param key
	 *            the key
	 * @return node holding key, or null if no such
	 */
	private Node<K, V> findNode(Comparable<? super K> key) {
		for (;;) {
			Node<K, V> b = findPredecessor(key);
			Node<K, V> n = b.next;
			for (;;) {
				if (n == null)
					return null;
				Node<K, V> f = n.next;
				if (n != b.next) // inconsistent read
					break;
				Object v = n.value;
				if (v == null) { // n is deleted
					n.helpDelete(b, f);
					break;
				}
				if (v == n || b.value == null) // b is deleted
					break;
				int c = key.compareTo(n.key);
				if (c == 0)
					return n;
				if (c < 0)
					return null;
				b = n;
				n = f;
			}
		}
	}

	void finishCount2(int nodesTraversed) {
		Vars vars = counts.get();
		vars.nodesTraversed += nodesTraversed;
	}

	void finishCount1(int nodesTraversed) {
		Vars vars = counts.get();
		vars.getCount++;
		vars.nodesTraversed += nodesTraversed;
	}

	// Extra version so we count the get traversals
	private Node<K, V> findGetNode(Comparable<? super K> key) {
		int nodesTraversed = 0;
		for (;;) {
			Node<K, V> b = findPredecessor(key);
			Node<K, V> n = b.next;
			if (TRAVERSAL_COUNT) {
				nodesTraversed++;
			}
			for (;;) {
				if (n == null) {
					if (TRAVERSAL_COUNT) {
						finishCount2(nodesTraversed);
					}
					return null;
				}
				Node<K, V> f = n.next;
				if (TRAVERSAL_COUNT) {
					nodesTraversed++;
				}
				if (n != b.next) // inconsistent read
					break;
				Object v = n.value;
				if (v == null) { // n is deleted
					n.helpDelete(b, f);
					break;
				}
				if (v == n || b.value == null) // b is deleted
					break;
				int c = key.compareTo(n.key);
				if (c == 0) {
					if (TRAVERSAL_COUNT) {
						finishCount2(nodesTraversed);
					}
					return n;
				}
				if (c < 0) {
					if (TRAVERSAL_COUNT) {
						finishCount2(nodesTraversed);
					}
					return null;
				}
				b = n;
				n = f;
			}
		}
	}

	/**
	 * Specialized variant of findNode to perform Map.get. Does a weak
	 * traversal, not bothering to fix any deleted index nodes, returning early
	 * if it happens to see key in index, and passing over any deleted base
	 * nodes, falling back to getUsingFindNode only if it would otherwise return
	 * value from an ongoing deletion. Also uses "bound" to eliminate need for
	 * some comparisons (see Pugh Cookbook). Also folds uses of null checks and
	 * node-skipping because markers have null keys.
	 * 
	 * @param okey
	 *            the key
	 * @return the value, or null if absent
	 */
	private V doGet(Object okey) {
		Comparable<? super K> key = comparable(okey);
		Node<K, V> bound = null;
		Index<K, V> q = head;
		Index<K, V> r = q.right;
		Node<K, V> n;
		K k;
		int c;

		int nodesTraversed = 0;
		if (TRAVERSAL_COUNT) {
			nodesTraversed++;
		}

		for (;;) {
			Index<K, V> d;
			// Traverse rights
			if (r != null && (n = r.node) != bound && (k = n.key) != null) {
				if ((c = key.compareTo(k)) > 0) {
					q = r;
					r = r.right;
					if (TRAVERSAL_COUNT) {
						nodesTraversed++;
					}
					continue;
				} else if (c == 0) {
					Object v = n.value;
					if (TRAVERSAL_COUNT) {
						finishCount1(nodesTraversed);
					}
					return (v != null) ? (V) v : getUsingFindNode(key);
				} else
					bound = n;
			}

			// Traverse down
			if ((d = q.down) != null) {
				q = d;
				r = d.right;
				if (TRAVERSAL_COUNT) {
					nodesTraversed++;
				}
			} else
				break;
		}

		// Traverse nexts
		for (n = q.node.next; n != null; n = n.next) {
			if (TRAVERSAL_COUNT) {
				nodesTraversed++;
			}
			if ((k = n.key) != null) {
				if ((c = key.compareTo(k)) == 0) {
					Object v = n.value;
					if (TRAVERSAL_COUNT) {
						finishCount1(nodesTraversed);
					}
					return (v != null) ? (V) v : getUsingFindNode(key);
				} else if (c < 0)
					break;
			}
		}
		if (TRAVERSAL_COUNT) {
			finishCount1(nodesTraversed);
		}
		return null;
	}

	/**
	 * Performs map.get via findNode. Used as a backup if doGet encounters an
	 * in-progress deletion.
	 * 
	 * @param key
	 *            the key
	 * @return the value, or null if absent
	 */
	private V getUsingFindNode(Comparable<? super K> key) {
		/*
		 * Loop needed here and elsewhere in case value field goes null just as
		 * it is about to be returned, in which case we lost a race with a
		 * deletion, so must retry.
		 */
		for (;;) {
			Node<K, V> n = findGetNode(key);
			if (n == null)
				return null;
			Object v = n.value;
			if (v != null)
				return (V) v;
		}
	}

	/* ---------------- Insertion -------------- */

	/**
	 * Main insertion method. Adds element if not present, or replaces value if
	 * present and onlyIfAbsent is false.
	 * 
	 * @param kkey
	 *            the key
	 * @param value
	 *            the value that must be associated with key
	 * @param onlyIfAbsent
	 *            if should not insert if already present
	 * @return the old value, or null if newly inserted
	 */
	private V doPut(K kkey, V value, boolean onlyIfAbsent) {
		Comparable<? super K> key = comparable(kkey);
		for (;;) {
			Node<K, V> b = findPredecessor(key);
			Node<K, V> n = b.next;
			for (;;) {
				if (n != null) {
					Node<K, V> f = n.next;
					if (n != b.next) // inconsistent read
						break;
					;
					Object v = n.value;
					if (v == null) { // n is deleted
						n.helpDelete(b, f);
						break;
					}
					if (v == n || b.value == null) // b is deleted
						break;
					int c = key.compareTo(n.key);
					if (c > 0) {
						b = n;
						n = f;
						continue;
					}
					if (c == 0) {
						if (onlyIfAbsent || n.casValue(v, value))
							return (V) v;
						else
							break; // restart if lost race to replace value
					}
					// else c < 0; fall through
				}

				Node<K, V> z = new Node<K, V>(kkey, value, n);
				if (!b.casNext(n, z))
					break; // restart if lost race to append to b
				int level = randomLevel();
				if (level > 0) {
					// if(STRUCT_MODS)
					// counts.get().structMods += level - 1;
					insertIndex(z, level);
				}
				return null;
			}
		}
	}

	/**
	 * Returns a random level for inserting a new node. Hardwired to k=1, p=0.5,
	 * max 31 (see above and Pugh's "Skip List Cookbook", sec 3.4).
	 * 
	 * This uses the simplest of the generators described in George Marsaglia's
	 * "Xorshift RNGs" paper. This is not a high-quality generator but is
	 * acceptable here.
	 */
	private int randomLevel() {
		int x = randomSeed;
		x ^= x << 13;
		x ^= x >>> 17;
		randomSeed = x ^= x << 5;
		if ((x & 0x8001) != 0) // test highest and lowest bits
			return 0;
		int level = 1;
		while (((x >>>= 1) & 1) != 0)
			++level;
		return level;
	}

	/**
	 * Creates and adds index nodes for the given node.
	 * 
	 * @param z
	 *            the node
	 * @param level
	 *            the level of the index
	 */
	private void insertIndex(Node<K, V> z, int level) {
		HeadIndex<K, V> h = head;
		int max = h.level;

		if (level <= max) {
			Index<K, V> idx = null;
			for (int i = 1; i <= level; ++i)
				idx = new Index<K, V>(z, idx, null);
			addIndex(idx, h, level);

		} else { // Add a new level
			/*
			 * To reduce interference by other threads checking for empty levels
			 * in tryReduceLevel, new levels are added with initialized right
			 * pointers. Which in turn requires keeping levels in an array to
			 * access them while creating new head index nodes from the opposite
			 * direction.
			 */
			level = max + 1;
			Index<K, V>[] idxs = (Index<K, V>[]) new Index[level + 1];
			Index<K, V> idx = null;
			for (int i = 1; i <= level; ++i)
				idxs[i] = idx = new Index<K, V>(z, idx, null);

			HeadIndex<K, V> oldh;
			int k;
			for (;;) {
				oldh = head;
				int oldLevel = oldh.level;
				if (level <= oldLevel) { // lost race to add level
					k = level;
					break;
				}
				HeadIndex<K, V> newh = oldh;
				Node<K, V> oldbase = oldh.node;
				for (int j = oldLevel + 1; j <= level; ++j)
					newh = new HeadIndex<K, V>(oldbase, newh, idxs[j], j);
				if (casHead(oldh, newh)) {
					k = oldLevel;
					break;
				}
			}
			addIndex(idxs[k], oldh, k);
		}
	}

	/**
	 * Adds given index nodes from given level down to 1.
	 * 
	 * @param idx
	 *            the topmost index node being inserted
	 * @param h
	 *            the value of head to use to insert. This must be snapshotted
	 *            by callers to provide correct insertion level
	 * @param indexLevel
	 *            the level of the index
	 */
	private void addIndex(Index<K, V> idx, HeadIndex<K, V> h, int indexLevel) {
		// Track next level to insert in case of retries
		int insertionLevel = indexLevel;
		Comparable<? super K> key = comparable(idx.node.key);
		if (key == null)
			throw new NullPointerException();

		// Similar to findPredecessor, but adding index nodes along
		// path to key.
		for (;;) {
			int j = h.level;
			Index<K, V> q = h;
			Index<K, V> r = q.right;
			Index<K, V> t = idx;
			for (;;) {
				if (r != null) {
					Node<K, V> n = r.node;
					// compare before deletion check avoids needing recheck
					int c = key.compareTo(n.key);
					if (n.value == null) {
						if (!q.unlink(r))
							break;
						r = q.right;
						continue;
					}
					if (c > 0) {
						q = r;
						r = r.right;
						continue;
					}
				}

				if (j == insertionLevel) {
					// Don't insert index if node already deleted
					if (t.indexesDeletedNode()) {
						findNode(key); // cleans up
						return;
					}
					if (!q.link(r, t))
						break; // restart
					if (--insertionLevel == 0) {
						// need final deletion check before return
						if (t.indexesDeletedNode())
							findNode(key);
						return;
					}
				}

				if (--j >= insertionLevel && j < indexLevel)
					t = t.down;
				q = q.down;
				r = q.right;
			}
		}
	}

	/* ---------------- Deletion -------------- */

	/**
	 * Main deletion method. Locates node, nulls value, appends a deletion
	 * marker, unlinks predecessor, removes associated index nodes, and possibly
	 * reduces head index level.
	 * 
	 * Index nodes are cleared out simply by calling findPredecessor. which
	 * unlinks indexes to deleted nodes found along path to key, which will
	 * include the indexes to this node. This is done unconditionally. We can't
	 * check beforehand whether there are index nodes because it might be the
	 * case that some or all indexes hadn't been inserted yet for this node
	 * during initial search for it, and we'd like to ensure lack of garbage
	 * retention, so must call to be sure.
	 * 
	 * @param okey
	 *            the key
	 * @param value
	 *            if non-null, the value that must be associated with key
	 * @return the node, or null if not found
	 */
	final V doRemove(Object okey, Object value) {
		Comparable<? super K> key = comparable(okey);
		for (;;) {
			Node<K, V> b = findPredecessor(key);
			Node<K, V> n = b.next;
			for (;;) {
				if (n == null)
					return null;
				Node<K, V> f = n.next;
				if (n != b.next) // inconsistent read
					break;
				Object v = n.value;
				if (v == null) { // n is deleted
					n.helpDelete(b, f);
					break;
				}
				if (v == n || b.value == null) // b is deleted
					break;
				int c = key.compareTo(n.key);
				if (c < 0)
					return null;
				if (c > 0) {
					b = n;
					n = f;
					continue;
				}
				if (value != null && !value.equals(v))
					return null;
				if (!n.casValue(v, null))
					break;
				if (STRUCT_MODS) {
					Vars vars = counts.get();
					vars.structMods++;
				}
				if (!n.appendMarker(f) || !b.casNext(n, f))
					findNode(key); // Retry via findNode
				else {
					findPredecessor(key); // Clean index
					if (head.right == null)
						tryReduceLevel();
				}
				return (V) v;
			}
		}
	}

	/**
	 * Possibly reduce head level if it has no nodes. This method can (rarely)
	 * make mistakes, in which case levels can disappear even though they are
	 * about to contain index nodes. This impacts performance, not correctness.
	 * To minimize mistakes as well as to reduce hysteresis, the level is
	 * reduced by one only if the topmost three levels look empty. Also, if the
	 * removed level looks non-empty after CAS, we try to change it back quick
	 * before anyone notices our mistake! (This trick works pretty well because
	 * this method will practically never make mistakes unless current thread
	 * stalls immediately before first CAS, in which case it is very unlikely to
	 * stall again immediately afterwards, so will recover.)
	 * 
	 * We put up with all this rather than just let levels grow because
	 * otherwise, even a small map that has undergone a large number of
	 * insertions and removals will have a lot of levels, slowing down access
	 * more than would an occasional unwanted reduction.
	 */
	private void tryReduceLevel() {
		HeadIndex<K, V> h = head;
		HeadIndex<K, V> d;
		HeadIndex<K, V> e;
		if (h.level > 3 && (d = (HeadIndex<K, V>) h.down) != null
				&& (e = (HeadIndex<K, V>) d.down) != null && e.right == null
				&& d.right == null && h.right == null && casHead(h, d) && // try
																			// to
																			// set
				h.right != null) // recheck
			casHead(d, h); // try to backout
	}

	/* ---------------- Finding and removing first element -------------- */

	/**
	 * Specialized variant of findNode to get first valid node.
	 * 
	 * @return first node or null if empty
	 */
	Node<K, V> findFirst() {
		for (;;) {
			Node<K, V> b = head.node;
			Node<K, V> n = b.next;
			if (n == null)
				return null;
			if (n.value != null)
				return n;
			n.helpDelete(b, n.next);
		}
	}

	/**
	 * Removes first entry; returns its snapshot.
	 * 
	 * @return null if empty, else snapshot of first entry
	 */
	Map.Entry<K, V> doRemoveFirstEntry() {
		for (;;) {
			Node<K, V> b = head.node;
			Node<K, V> n = b.next;
			if (n == null)
				return null;
			Node<K, V> f = n.next;
			if (n != b.next)
				continue;
			Object v = n.value;
			if (v == null) {
				n.helpDelete(b, f);
				continue;
			}
			if (!n.casValue(v, null))
				continue;
			if (!n.appendMarker(f) || !b.casNext(n, f))
				findFirst(); // retry
			clearIndexToFirst();
			return new AbstractMap.SimpleImmutableEntry<K, V>(n.key, (V) v);
		}
	}

	/**
	 * Clears out index nodes associated with deleted first entry.
	 */
	private void clearIndexToFirst() {
		for (;;) {
			Index<K, V> q = head;
			for (;;) {
				Index<K, V> r = q.right;
				if (r != null && r.indexesDeletedNode() && !q.unlink(r))
					break;
				if ((q = q.down) == null) {
					if (head.right == null)
						tryReduceLevel();
					return;
				}
			}
		}
	}

	/* ---------------- Finding and removing last element -------------- */

	/**
	 * Specialized version of find to get last valid node.
	 * 
	 * @return last node or null if empty
	 */
	Node<K, V> findLast() {
		/*
		 * findPredecessor can't be used to traverse index level because this
		 * doesn't use comparisons. So traversals of both levels are folded
		 * together.
		 */
		Index<K, V> q = head;
		for (;;) {
			Index<K, V> d, r;
			if ((r = q.right) != null) {
				if (r.indexesDeletedNode()) {
					q.unlink(r);
					q = head; // restart
				} else
					q = r;
			} else if ((d = q.down) != null) {
				q = d;
			} else {
				Node<K, V> b = q.node;
				Node<K, V> n = b.next;
				for (;;) {
					if (n == null)
						return (b.isBaseHeader()) ? null : b;
					Node<K, V> f = n.next; // inconsistent read
					if (n != b.next)
						break;
					Object v = n.value;
					if (v == null) { // n is deleted
						n.helpDelete(b, f);
						break;
					}
					if (v == n || b.value == null) // b is deleted
						break;
					b = n;
					n = f;
				}
				q = head; // restart
			}
		}
	}

	/**
	 * Specialized variant of findPredecessor to get predecessor of last valid
	 * node. Needed when removing the last entry. It is possible that all
	 * successors of returned node will have been deleted upon return, in which
	 * case this method can be retried.
	 * 
	 * @return likely predecessor of last node
	 */
	private Node<K, V> findPredecessorOfLast() {
		for (;;) {
			Index<K, V> q = head;
			for (;;) {
				Index<K, V> d, r;
				if ((r = q.right) != null) {
					if (r.indexesDeletedNode()) {
						q.unlink(r);
						break; // must restart
					}
					// proceed as far across as possible without overshooting
					if (r.node.next != null) {
						q = r;
						continue;
					}
				}
				if ((d = q.down) != null)
					q = d;
				else
					return q.node;
			}
		}
	}

	/**
	 * Removes last entry; returns its snapshot. Specialized variant of
	 * doRemove.
	 * 
	 * @return null if empty, else snapshot of last entry
	 */
	Map.Entry<K, V> doRemoveLastEntry() {
		for (;;) {
			Node<K, V> b = findPredecessorOfLast();
			Node<K, V> n = b.next;
			if (n == null) {
				if (b.isBaseHeader()) // empty
					return null;
				else
					continue; // all b's successors are deleted; retry
			}
			for (;;) {
				Node<K, V> f = n.next;
				if (n != b.next) // inconsistent read
					break;
				Object v = n.value;
				if (v == null) { // n is deleted
					n.helpDelete(b, f);
					break;
				}
				if (v == n || b.value == null) // b is deleted
					break;
				if (f != null) {
					b = n;
					n = f;
					continue;
				}
				if (!n.casValue(v, null))
					break;
				K key = n.key;
				Comparable<? super K> ck = comparable(key);
				if (!n.appendMarker(f) || !b.casNext(n, f))
					findNode(ck); // Retry via findNode
				else {
					findPredecessor(ck); // Clean index
					if (head.right == null)
						tryReduceLevel();
				}
				return new AbstractMap.SimpleImmutableEntry<K, V>(key, (V) v);
			}
		}
	}

	/* ---------------- Relational operations -------------- */

	// Control values OR'ed as arguments to findNear
	private static final int EQ = 1;
	private static final int LT = 2;
	private static final int GT = 0; // Actually checked as !LT

	/**
	 * Utility for ceiling, floor, lower, higher methods.
	 * 
	 * @param kkey
	 *            the key
	 * @param rel
	 *            the relation -- OR'ed combination of EQ, LT, GT
	 * @return nearest node fitting relation, or null if no such
	 */
	Node<K, V> findNear(K kkey, int rel) {
		Comparable<? super K> key = comparable(kkey);
		for (;;) {
			Node<K, V> b = findPredecessor(key);
			Node<K, V> n = b.next;
			for (;;) {
				if (n == null)
					return ((rel & LT) == 0 || b.isBaseHeader()) ? null : b;
				Node<K, V> f = n.next;
				if (n != b.next) // inconsistent read
					break;
				Object v = n.value;
				if (v == null) { // n is deleted
					n.helpDelete(b, f);
					break;
				}
				if (v == n || b.value == null) // b is deleted
					break;
				int c = key.compareTo(n.key);
				if ((c == 0 && (rel & EQ) != 0) || (c < 0 && (rel & LT) == 0))
					return n;
				if (c <= 0 && (rel & LT) != 0)
					return (b.isBaseHeader()) ? null : b;
				b = n;
				n = f;
			}
		}
	}

	/**
	 * Returns SimpleImmutableEntry for results of findNear.
	 * 
	 * @param key
	 *            the key
	 * @param rel
	 *            the relation -- OR'ed combination of EQ, LT, GT
	 * @return Entry fitting relation, or null if no such
	 */
	AbstractMap.SimpleImmutableEntry<K, V> getNear(K key, int rel) {
		for (;;) {
			Node<K, V> n = findNear(key, rel);
			if (n == null)
				return null;
			AbstractMap.SimpleImmutableEntry<K, V> e = n.createSnapshot();
			if (e != null)
				return e;
		}
	}

	/* ---------------- Constructors -------------- */

	/**
	 * Constructs a new, empty map, sorted according to the
	 * {@linkplain Comparable natural ordering} of the keys.
	 */
	public NonBlockingJavaSkipListMap() {
		this.comparator = null;
		initialize();
	}

	/**
	 * Constructs a new, empty map, sorted according to the specified
	 * comparator.
	 * 
	 * @param comparator
	 *            the comparator that will be used to order this map. If
	 *            <tt>null</tt>, the {@linkplain Comparable natural ordering} of
	 *            the keys will be used.
	 */
	public NonBlockingJavaSkipListMap(Comparator<? super K> comparator) {
		this.comparator = comparator;
		initialize();
	}

	/**
	 * Constructs a new map containing the same mappings as the given map,
	 * sorted according to the {@linkplain Comparable natural ordering} of the
	 * keys.
	 * 
	 * @param m
	 *            the map whose mappings are to be placed in this map
	 * @throws ClassCastException
	 *             if the keys in <tt>m</tt> are not {@link Comparable}, or are
	 *             not mutually comparable
	 * @throws NullPointerException
	 *             if the specified map or any of its keys or values are null
	 */
	public NonBlockingJavaSkipListMap(Map<? extends K, ? extends V> m) {
		this.comparator = null;
		initialize();
		putAll(m);
	}

	/**
	 * Constructs a new map containing the same mappings and using the same
	 * ordering as the specified sorted map.
	 * 
	 * @param m
	 *            the sorted map whose mappings are to be placed in this map,
	 *            and whose comparator is to be used to sort this map
	 * @throws NullPointerException
	 *             if the specified sorted map or any of its keys or values are
	 *             null
	 */
	public NonBlockingJavaSkipListMap(SortedMap<K, ? extends V> m) {
		this.comparator = m.comparator();
		initialize();
		buildFromSorted(m);
	}

	/**
	 * Returns a shallow copy of this <tt>ConcurrentSkipListMap</tt> instance.
	 * (The keys and values themselves are not cloned.)
	 * 
	 * @return a shallow copy of this map
	 */
	public NonBlockingJavaSkipListMap<K, V> clone() {
		NonBlockingJavaSkipListMap<K, V> clone = null;
		try {
			clone = (NonBlockingJavaSkipListMap<K, V>) super.clone();
		} catch (CloneNotSupportedException e) {
			throw new InternalError();
		}

		clone.initialize();
		clone.buildFromSorted(this);
		return clone;
	}

	/**
	 * Streamlined bulk insertion to initialize from elements of given sorted
	 * map. Call only from constructor or clone method.
	 */
	private void buildFromSorted(SortedMap<K, ? extends V> map) {
		if (map == null)
			throw new NullPointerException();

		HeadIndex<K, V> h = head;
		Node<K, V> basepred = h.node;

		// Track the current rightmost node at each level. Uses an
		// ArrayList to avoid committing to initial or maximum level.
		ArrayList<Index<K, V>> preds = new ArrayList<Index<K, V>>();

		// initialize
		for (int i = 0; i <= h.level; ++i)
			preds.add(null);
		Index<K, V> q = h;
		for (int i = h.level; i > 0; --i) {
			preds.set(i, q);
			q = q.down;
		}

		Iterator<? extends Map.Entry<? extends K, ? extends V>> it = map
				.entrySet().iterator();
		while (it.hasNext()) {
			Map.Entry<? extends K, ? extends V> e = it.next();
			int j = randomLevel();
			if (j > h.level)
				j = h.level + 1;
			K k = e.getKey();
			V v = e.getValue();
			if (k == null || v == null)
				throw new NullPointerException();
			Node<K, V> z = new Node<K, V>(k, v, null);
			basepred.next = z;
			basepred = z;
			if (j > 0) {
				Index<K, V> idx = null;
				for (int i = 1; i <= j; ++i) {
					idx = new Index<K, V>(z, idx, null);
					if (i > h.level)
						h = new HeadIndex<K, V>(h.node, h, idx, i);

					if (i < preds.size()) {
						preds.get(i).right = idx;
						preds.set(i, idx);
					} else
						preds.add(idx);
				}
			}
		}
		head = h;
	}

	/* ---------------- Serialization -------------- */

	/**
	 * Save the state of this map to a stream.
	 * 
	 * @serialData The key (Object) and value (Object) for each key-value
	 *             mapping represented by the map, followed by <tt>null</tt>.
	 *             The key-value mappings are emitted in key-order (as
	 *             determined by the Comparator, or by the keys' natural
	 *             ordering if no Comparator).
	 */
	private void writeObject(java.io.ObjectOutputStream s)
			throws java.io.IOException {
		// Write out the Comparator and any hidden stuff
		s.defaultWriteObject();

		// Write out keys and values (alternating)
		for (Node<K, V> n = findFirst(); n != null; n = n.next) {
			V v = n.getValidValue();
			if (v != null) {
				s.writeObject(n.key);
				s.writeObject(v);
			}
		}
		s.writeObject(null);
	}

	/**
	 * Reconstitute the map from a stream.
	 */
	private void readObject(final java.io.ObjectInputStream s)
			throws java.io.IOException, ClassNotFoundException {
		// Read in the Comparator and any hidden stuff
		s.defaultReadObject();
		// Reset transients
		initialize();

		/*
		 * This is nearly identical to buildFromSorted, but is distinct because
		 * readObject calls can't be nicely adapted as the kind of iterator
		 * needed by buildFromSorted. (They can be, but doing so requires type
		 * cheats and/or creation of adaptor classes.) It is simpler to just
		 * adapt the code.
		 */

		HeadIndex<K, V> h = head;
		Node<K, V> basepred = h.node;
		ArrayList<Index<K, V>> preds = new ArrayList<Index<K, V>>();
		for (int i = 0; i <= h.level; ++i)
			preds.add(null);
		Index<K, V> q = h;
		for (int i = h.level; i > 0; --i) {
			preds.set(i, q);
			q = q.down;
		}

		for (;;) {
			Object k = s.readObject();
			if (k == null)
				break;
			Object v = s.readObject();
			if (v == null)
				throw new NullPointerException();
			K key = (K) k;
			V val = (V) v;
			int j = randomLevel();
			if (j > h.level)
				j = h.level + 1;
			Node<K, V> z = new Node<K, V>(key, val, null);
			basepred.next = z;
			basepred = z;
			if (j > 0) {
				Index<K, V> idx = null;
				for (int i = 1; i <= j; ++i) {
					idx = new Index<K, V>(z, idx, null);
					if (i > h.level)
						h = new HeadIndex<K, V>(h.node, h, idx, i);

					if (i < preds.size()) {
						preds.get(i).right = idx;
						preds.set(i, idx);
					} else
						preds.add(idx);
				}
			}
		}
		head = h;
	}

	/* ------ Map API methods ------ */

	/**
	 * Returns <tt>true</tt> if this map contains a mapping for the specified
	 * key.
	 * 
	 * @param key
	 *            key whose presence in this map is to be tested
	 * @return <tt>true</tt> if this map contains a mapping for the specified
	 *         key
	 * @throws ClassCastException
	 *             if the specified key cannot be compared with the keys
	 *             currently in the map
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public boolean containsKey(Object key) {
		return doGet(key) != null;
	}

	/**
	 * Returns the value to which the specified key is mapped, or {@code null}
	 * if this map contains no mapping for the key.
	 * 
	 * <p>
	 * More formally, if this map contains a mapping from a key {@code k} to a
	 * value {@code v} such that {@code key} compares equal to {@code k}
	 * according to the map's ordering, then this method returns {@code v};
	 * otherwise it returns {@code null}. (There can be at most one such
	 * mapping.)
	 * 
	 * @throws ClassCastException
	 *             if the specified key cannot be compared with the keys
	 *             currently in the map
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public V get(Object key) {
		return doGet(key);
	}

	/**
	 * Associates the specified value with the specified key in this map. If the
	 * map previously contained a mapping for the key, the old value is
	 * replaced.
	 * 
	 * @param key
	 *            key with which the specified value is to be associated
	 * @param value
	 *            value to be associated with the specified key
	 * @return the previous value associated with the specified key, or
	 *         <tt>null</tt> if there was no mapping for the key
	 * @throws ClassCastException
	 *             if the specified key cannot be compared with the keys
	 *             currently in the map
	 * @throws NullPointerException
	 *             if the specified key or value is null
	 */
	public V put(K key, V value) {
		if (value == null)
			throw new NullPointerException();
		return doPut(key, value, false);
	}

	/**
	 * Removes the mapping for the specified key from this map if present.
	 * 
	 * @param key
	 *            key for which mapping should be removed
	 * @return the previous value associated with the specified key, or
	 *         <tt>null</tt> if there was no mapping for the key
	 * @throws ClassCastException
	 *             if the specified key cannot be compared with the keys
	 *             currently in the map
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public V remove(Object key) {
		return doRemove(key, null);
	}

	/**
	 * Returns <tt>true</tt> if this map maps one or more keys to the specified
	 * value. This operation requires time linear in the map size.
	 * 
	 * @param value
	 *            value whose presence in this map is to be tested
	 * @return <tt>true</tt> if a mapping to <tt>value</tt> exists;
	 *         <tt>false</tt> otherwise
	 * @throws NullPointerException
	 *             if the specified value is null
	 */
	public boolean containsValue(Object value) {
		if (value == null)
			throw new NullPointerException();
		for (Node<K, V> n = findFirst(); n != null; n = n.next) {
			V v = n.getValidValue();
			if (v != null && value.equals(v))
				return true;
		}
		return false;
	}

	/**
	 * Returns the number of key-value mappings in this map. If this map
	 * contains more than <tt>Integer.MAX_VALUE</tt> elements, it returns
	 * <tt>Integer.MAX_VALUE</tt>.
	 * 
	 * <p>
	 * Beware that, unlike in most collections, this method is <em>NOT</em> a
	 * constant-time operation. Because of the asynchronous nature of these
	 * maps, determining the current number of elements requires traversing them
	 * all to count them. Additionally, it is possible for the size to change
	 * during execution of this method, in which case the returned result will
	 * be inaccurate. Thus, this method is typically not very useful in
	 * concurrent applications.
	 * 
	 * @return the number of elements in this map
	 */
	public int size() {
		long count = 0;
		for (Node<K, V> n = findFirst(); n != null; n = n.next) {
			if (n.getValidValue() != null)
				++count;
		}
		return (count >= Integer.MAX_VALUE) ? Integer.MAX_VALUE : (int) count;
	}

	/**
	 * Returns <tt>true</tt> if this map contains no key-value mappings.
	 * 
	 * @return <tt>true</tt> if this map contains no key-value mappings
	 */
	public boolean isEmpty() {
		return findFirst() == null;
	}

	/**
	 * Removes all of the mappings from this map.
	 */
	public void clear() {
		initialize();
	}

	/* ---------------- View methods -------------- */

	/*
	 * Note: Lazy initialization works for views because view classes are
	 * stateless/immutable so it doesn't matter wrt correctness if more than one
	 * is created (which will only rarely happen). Even so, the following idiom
	 * conservatively ensures that the method returns the one it created if it
	 * does so, not one created by another racing thread.
	 */

	/**
	 * Returns a {@link NavigableSet} view of the keys contained in this map.
	 * The set's iterator returns the keys in ascending order. The set is backed
	 * by the map, so changes to the map are reflected in the set, and
	 * vice-versa. The set supports element removal, which removes the
	 * corresponding mapping from the map, via the {@code Iterator.remove},
	 * {@code Set.remove}, {@code removeAll}, {@code retainAll}, and
	 * {@code clear} operations. It does not support the {@code add} or
	 * {@code addAll} operations.
	 * 
	 * <p>
	 * The view's {@code iterator} is a "weakly consistent" iterator that will
	 * never throw {@link ConcurrentModificationException}, and guarantees to
	 * traverse elements as they existed upon construction of the iterator, and
	 * may (but is not guaranteed to) reflect any modifications subsequent to
	 * construction.
	 * 
	 * <p>
	 * This method is equivalent to method {@code navigableKeySet}.
	 * 
	 * @return a navigable set view of the keys in this map
	 */
	public NavigableSet<K> keySet() {
		KeySet ks = keySet;
		return (ks != null) ? ks : (keySet = new KeySet(this));
	}

	public NavigableSet<K> navigableKeySet() {
		KeySet ks = keySet;
		return (ks != null) ? ks : (keySet = new KeySet(this));
	}

	/**
	 * Returns a {@link Collection} view of the values contained in this map.
	 * The collection's iterator returns the values in ascending order of the
	 * corresponding keys. The collection is backed by the map, so changes to
	 * the map are reflected in the collection, and vice-versa. The collection
	 * supports element removal, which removes the corresponding mapping from
	 * the map, via the <tt>Iterator.remove</tt>, <tt>Collection.remove</tt>,
	 * <tt>removeAll</tt>, <tt>retainAll</tt> and <tt>clear</tt> operations. It
	 * does not support the <tt>add</tt> or <tt>addAll</tt> operations.
	 * 
	 * <p>
	 * The view's <tt>iterator</tt> is a "weakly consistent" iterator that will
	 * never throw {@link ConcurrentModificationException}, and guarantees to
	 * traverse elements as they existed upon construction of the iterator, and
	 * may (but is not guaranteed to) reflect any modifications subsequent to
	 * construction.
	 */
	public Collection<V> values() {
		Values vs = values;
		return (vs != null) ? vs : (values = new Values(this));
	}

	/**
	 * Returns a {@link Set} view of the mappings contained in this map. The
	 * set's iterator returns the entries in ascending key order. The set is
	 * backed by the map, so changes to the map are reflected in the set, and
	 * vice-versa. The set supports element removal, which removes the
	 * corresponding mapping from the map, via the <tt>Iterator.remove</tt>,
	 * <tt>Set.remove</tt>, <tt>removeAll</tt>, <tt>retainAll</tt> and
	 * <tt>clear</tt> operations. It does not support the <tt>add</tt> or
	 * <tt>addAll</tt> operations.
	 * 
	 * <p>
	 * The view's <tt>iterator</tt> is a "weakly consistent" iterator that will
	 * never throw {@link ConcurrentModificationException}, and guarantees to
	 * traverse elements as they existed upon construction of the iterator, and
	 * may (but is not guaranteed to) reflect any modifications subsequent to
	 * construction.
	 * 
	 * <p>
	 * The <tt>Map.Entry</tt> elements returned by <tt>iterator.next()</tt> do
	 * <em>not</em> support the <tt>setValue</tt> operation.
	 * 
	 * @return a set view of the mappings contained in this map, sorted in
	 *         ascending key order
	 */
	public Set<Map.Entry<K, V>> entrySet() {
		EntrySet es = entrySet;
		return (es != null) ? es : (entrySet = new EntrySet(this));
	}

	public ConcurrentNavigableMap<K, V> descendingMap() {
		ConcurrentNavigableMap<K, V> dm = descendingMap;
		return (dm != null) ? dm : (descendingMap = new SubMap<K, V>(this,
				null, false, null, false, true));
	}

	public NavigableSet<K> descendingKeySet() {
		return descendingMap().navigableKeySet();
	}

	/* ---------------- AbstractMap Overrides -------------- */

	/**
	 * Compares the specified object with this map for equality. Returns
	 * <tt>true</tt> if the given object is also a map and the two maps
	 * represent the same mappings. More formally, two maps <tt>m1</tt> and
	 * <tt>m2</tt> represent the same mappings if
	 * <tt>m1.entrySet().equals(m2.entrySet())</tt>. This operation may return
	 * misleading results if either map is concurrently modified during
	 * execution of this method.
	 * 
	 * @param o
	 *            object to be compared for equality with this map
	 * @return <tt>true</tt> if the specified object is equal to this map
	 */
	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof Map))
			return false;
		Map<?, ?> m = (Map<?, ?>) o;
		try {
			for (Map.Entry<K, V> e : this.entrySet())
				if (!e.getValue().equals(m.get(e.getKey())))
					return false;
			for (Map.Entry<?, ?> e : m.entrySet()) {
				Object k = e.getKey();
				Object v = e.getValue();
				if (k == null || v == null || !v.equals(get(k)))
					return false;
			}
			return true;
		} catch (ClassCastException unused) {
			return false;
		} catch (NullPointerException unused) {
			return false;
		}
	}

	/* ------ ConcurrentMap API methods ------ */

	/**
	 * {@inheritDoc}
	 * 
	 * @return the previous value associated with the specified key, or
	 *         <tt>null</tt> if there was no mapping for the key
	 * @throws ClassCastException
	 *             if the specified key cannot be compared with the keys
	 *             currently in the map
	 * @throws NullPointerException
	 *             if the specified key or value is null
	 */
	public V putIfAbsent(K key, V value) {
		if (value == null)
			throw new NullPointerException();
		return doPut(key, value, true);
	}

	/**
	 * {@inheritDoc}
	 * 
	 * @throws ClassCastException
	 *             if the specified key cannot be compared with the keys
	 *             currently in the map
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public boolean remove(Object key, Object value) {
		if (key == null)
			throw new NullPointerException();
		if (value == null)
			return false;
		return doRemove(key, value) != null;
	}

	/**
	 * {@inheritDoc}
	 * 
	 * @throws ClassCastException
	 *             if the specified key cannot be compared with the keys
	 *             currently in the map
	 * @throws NullPointerException
	 *             if any of the arguments are null
	 */
	public boolean replace(K key, V oldValue, V newValue) {
		if (oldValue == null || newValue == null)
			throw new NullPointerException();
		Comparable<? super K> k = comparable(key);
		for (;;) {
			Node<K, V> n = findNode(k);
			if (n == null)
				return false;
			Object v = n.value;
			if (v != null) {
				if (!oldValue.equals(v))
					return false;
				if (n.casValue(v, newValue))
					return true;
			}
		}
	}

	/**
	 * {@inheritDoc}
	 * 
	 * @return the previous value associated with the specified key, or
	 *         <tt>null</tt> if there was no mapping for the key
	 * @throws ClassCastException
	 *             if the specified key cannot be compared with the keys
	 *             currently in the map
	 * @throws NullPointerException
	 *             if the specified key or value is null
	 */
	public V replace(K key, V value) {
		if (value == null)
			throw new NullPointerException();
		Comparable<? super K> k = comparable(key);
		for (;;) {
			Node<K, V> n = findNode(k);
			if (n == null)
				return null;
			Object v = n.value;
			if (v != null && n.casValue(v, value))
				return (V) v;
		}
	}

	/* ------ SortedMap API methods ------ */

	public Comparator<? super K> comparator() {
		return comparator;
	}

	/**
	 * @throws NoSuchElementException
	 *             {@inheritDoc}
	 */
	public K firstKey() {
		Node<K, V> n = findFirst();
		if (n == null)
			throw new NoSuchElementException();
		return n.key;
	}

	/**
	 * @throws NoSuchElementException
	 *             {@inheritDoc}
	 */
	public K lastKey() {
		Node<K, V> n = findLast();
		if (n == null)
			throw new NoSuchElementException();
		return n.key;
	}

	/**
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if {@code fromKey} or {@code toKey} is null
	 * @throws IllegalArgumentException
	 *             {@inheritDoc}
	 */
	public ConcurrentNavigableMap<K, V> subMap(K fromKey,
			boolean fromInclusive, K toKey, boolean toInclusive) {
		if (fromKey == null || toKey == null)
			throw new NullPointerException();
		return new SubMap<K, V>(this, fromKey, fromInclusive, toKey,
				toInclusive, false);
	}

	/**
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if {@code toKey} is null
	 * @throws IllegalArgumentException
	 *             {@inheritDoc}
	 */
	public ConcurrentNavigableMap<K, V> headMap(K toKey, boolean inclusive) {
		if (toKey == null)
			throw new NullPointerException();
		return new SubMap<K, V>(this, null, false, toKey, inclusive, false);
	}

	/**
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if {@code fromKey} is null
	 * @throws IllegalArgumentException
	 *             {@inheritDoc}
	 */
	public ConcurrentNavigableMap<K, V> tailMap(K fromKey, boolean inclusive) {
		if (fromKey == null)
			throw new NullPointerException();
		return new SubMap<K, V>(this, fromKey, inclusive, null, false, false);
	}

	/**
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if {@code fromKey} or {@code toKey} is null
	 * @throws IllegalArgumentException
	 *             {@inheritDoc}
	 */
	public ConcurrentNavigableMap<K, V> subMap(K fromKey, K toKey) {
		return subMap(fromKey, true, toKey, false);
	}

	/**
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if {@code toKey} is null
	 * @throws IllegalArgumentException
	 *             {@inheritDoc}
	 */
	public ConcurrentNavigableMap<K, V> headMap(K toKey) {
		return headMap(toKey, false);
	}

	/**
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if {@code fromKey} is null
	 * @throws IllegalArgumentException
	 *             {@inheritDoc}
	 */
	public ConcurrentNavigableMap<K, V> tailMap(K fromKey) {
		return tailMap(fromKey, true);
	}

	/* ---------------- Relational operations -------------- */

	/**
	 * Returns a key-value mapping associated with the greatest key strictly
	 * less than the given key, or <tt>null</tt> if there is no such key. The
	 * returned entry does <em>not</em> support the <tt>Entry.setValue</tt>
	 * method.
	 * 
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public Map.Entry<K, V> lowerEntry(K key) {
		return getNear(key, LT);
	}

	/**
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public K lowerKey(K key) {
		Node<K, V> n = findNear(key, LT);
		return (n == null) ? null : n.key;
	}

	/**
	 * Returns a key-value mapping associated with the greatest key less than or
	 * equal to the given key, or <tt>null</tt> if there is no such key. The
	 * returned entry does <em>not</em> support the <tt>Entry.setValue</tt>
	 * method.
	 * 
	 * @param key
	 *            the key
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public Map.Entry<K, V> floorEntry(K key) {
		return getNear(key, LT | EQ);
	}

	/**
	 * @param key
	 *            the key
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public K floorKey(K key) {
		Node<K, V> n = findNear(key, LT | EQ);
		return (n == null) ? null : n.key;
	}

	/**
	 * Returns a key-value mapping associated with the least key greater than or
	 * equal to the given key, or <tt>null</tt> if there is no such entry. The
	 * returned entry does <em>not</em> support the <tt>Entry.setValue</tt>
	 * method.
	 * 
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public Map.Entry<K, V> ceilingEntry(K key) {
		return getNear(key, GT | EQ);
	}

	/**
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public K ceilingKey(K key) {
		Node<K, V> n = findNear(key, GT | EQ);
		return (n == null) ? null : n.key;
	}

	/**
	 * Returns a key-value mapping associated with the least key strictly
	 * greater than the given key, or <tt>null</tt> if there is no such key. The
	 * returned entry does <em>not</em> support the <tt>Entry.setValue</tt>
	 * method.
	 * 
	 * @param key
	 *            the key
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public Map.Entry<K, V> higherEntry(K key) {
		return getNear(key, GT);
	}

	/**
	 * @param key
	 *            the key
	 * @throws ClassCastException
	 *             {@inheritDoc}
	 * @throws NullPointerException
	 *             if the specified key is null
	 */
	public K higherKey(K key) {
		Node<K, V> n = findNear(key, GT);
		return (n == null) ? null : n.key;
	}

	/**
	 * Returns a key-value mapping associated with the least key in this map, or
	 * <tt>null</tt> if the map is empty. The returned entry does <em>not</em>
	 * support the <tt>Entry.setValue</tt> method.
	 */
	public Map.Entry<K, V> firstEntry() {
		for (;;) {
			Node<K, V> n = findFirst();
			if (n == null)
				return null;
			AbstractMap.SimpleImmutableEntry<K, V> e = n.createSnapshot();
			if (e != null)
				return e;
		}
	}

	/**
	 * Returns a key-value mapping associated with the greatest key in this map,
	 * or <tt>null</tt> if the map is empty. The returned entry does
	 * <em>not</em> support the <tt>Entry.setValue</tt> method.
	 */
	public Map.Entry<K, V> lastEntry() {
		for (;;) {
			Node<K, V> n = findLast();
			if (n == null)
				return null;
			AbstractMap.SimpleImmutableEntry<K, V> e = n.createSnapshot();
			if (e != null)
				return e;
		}
	}

	/**
	 * Removes and returns a key-value mapping associated with the least key in
	 * this map, or <tt>null</tt> if the map is empty. The returned entry does
	 * <em>not</em> support the <tt>Entry.setValue</tt> method.
	 */
	public Map.Entry<K, V> pollFirstEntry() {
		return doRemoveFirstEntry();
	}

	/**
	 * Removes and returns a key-value mapping associated with the greatest key
	 * in this map, or <tt>null</tt> if the map is empty. The returned entry
	 * does <em>not</em> support the <tt>Entry.setValue</tt> method.
	 */
	public Map.Entry<K, V> pollLastEntry() {
		return doRemoveLastEntry();
	}

	/* ---------------- Iterators -------------- */

	/**
	 * Base of iterator classes:
	 */
	abstract class Iter<T> implements Iterator<T> {
		/** the last node returned by next() */
		Node<K, V> lastReturned;
		/** the next node to return from next(); */
		Node<K, V> next;
		/** Cache of next value field to maintain weak consistency */
		V nextValue;

		/** Initializes ascending iterator for entire range. */
		Iter() {
			for (;;) {
				next = findFirst();
				if (next == null)
					break;
				Object x = next.value;
				if (x != null && x != next) {
					nextValue = (V) x;
					break;
				}
			}
		}

		public final boolean hasNext() {
			return next != null;
		}

		/** Advances next to higher entry. */
		final void advance() {
			if (next == null)
				throw new NoSuchElementException();
			lastReturned = next;
			for (;;) {
				next = next.next;
				if (next == null)
					break;
				Object x = next.value;
				if (x != null && x != next) {
					nextValue = (V) x;
					break;
				}
			}
		}

		public void remove() {
			Node<K, V> l = lastReturned;
			if (l == null)
				throw new IllegalStateException();
			// It would not be worth all of the overhead to directly
			// unlink from here. Using remove is fast enough.
			NonBlockingJavaSkipListMap.this.remove(l.key);
			lastReturned = null;
		}

	}

	final class ValueIterator extends Iter<V> {
		public V next() {
			V v = nextValue;
			advance();
			return v;
		}
	}

	final class KeyIterator extends Iter<K> {
		public K next() {
			Node<K, V> n = next;
			advance();
			return n.key;
		}
	}

	final class EntryIterator extends Iter<Map.Entry<K, V>> {
		public Map.Entry<K, V> next() {
			Node<K, V> n = next;
			V v = nextValue;
			advance();
			return new AbstractMap.SimpleImmutableEntry<K, V>(n.key, v);
		}
	}

	// Factory methods for iterators needed by ConcurrentSkipListSet etc

	Iterator<K> keyIterator() {
		return new KeyIterator();
	}

	Iterator<V> valueIterator() {
		return new ValueIterator();
	}

	Iterator<Map.Entry<K, V>> entryIterator() {
		return new EntryIterator();
	}

	/* ---------------- View Classes -------------- */

	/*
	 * View classes are static, delegating to a ConcurrentNavigableMap to allow
	 * use by SubMaps, which outweighs the ugliness of needing type-tests for
	 * Iterator methods.
	 */

	static final <E> List<E> toList(Collection<E> c) {
		// Using size() here would be a pessimization.
		List<E> list = new ArrayList<E>();
		for (E e : c)
			list.add(e);
		return list;
	}

	static final class KeySet<E> extends AbstractSet<E> implements
			NavigableSet<E> {
		private final ConcurrentNavigableMap<E, Object> m;

		KeySet(ConcurrentNavigableMap<E, Object> map) {
			m = map;
		}

		public int size() {
			return m.size();
		}

		public boolean isEmpty() {
			return m.isEmpty();
		}

		public boolean contains(Object o) {
			return m.containsKey(o);
		}

		public boolean remove(Object o) {
			return m.remove(o) != null;
		}

		public void clear() {
			m.clear();
		}

		public E lower(E e) {
			return m.lowerKey(e);
		}

		public E floor(E e) {
			return m.floorKey(e);
		}

		public E ceiling(E e) {
			return m.ceilingKey(e);
		}

		public E higher(E e) {
			return m.higherKey(e);
		}

		public Comparator<? super E> comparator() {
			return m.comparator();
		}

		public E first() {
			return m.firstKey();
		}

		public E last() {
			return m.lastKey();
		}

		public E pollFirst() {
			Map.Entry<E, Object> e = m.pollFirstEntry();
			return e == null ? null : e.getKey();
		}

		public E pollLast() {
			Map.Entry<E, Object> e = m.pollLastEntry();
			return e == null ? null : e.getKey();
		}

		public Iterator<E> iterator() {
			if (m instanceof NonBlockingJavaSkipListMap)
				return ((NonBlockingJavaSkipListMap<E, Object>) m)
						.keyIterator();
			else
				return ((NonBlockingJavaSkipListMap.SubMap<E, Object>) m)
						.keyIterator();
		}

		public boolean equals(Object o) {
			if (o == this)
				return true;
			if (!(o instanceof Set))
				return false;
			Collection<?> c = (Collection<?>) o;
			try {
				return containsAll(c) && c.containsAll(this);
			} catch (ClassCastException unused) {
				return false;
			} catch (NullPointerException unused) {
				return false;
			}
		}

		public Object[] toArray() {
			return toList(this).toArray();
		}

		public <T> T[] toArray(T[] a) {
			return toList(this).toArray(a);
		}

		public Iterator<E> descendingIterator() {
			return descendingSet().iterator();
		}

		public NavigableSet<E> subSet(E fromElement, boolean fromInclusive,
				E toElement, boolean toInclusive) {
			//TODO this is not implemented
			return null;
			// return new ConcurrentSkipListSet<E>(m.subMap(fromElement,
			// fromInclusive, toElement, toInclusive));
		}

		public NavigableSet<E> headSet(E toElement, boolean inclusive) {
			//TODO this is not implemented
			return null;
//			return new ConcurrentSkipListSet<E>(m.headMap(toElement, inclusive));
		}

		public NavigableSet<E> tailSet(E fromElement, boolean inclusive) {
			//TODO this is not implemented
			return null;
//			return new ConcurrentSkipListSet<E>(m.tailMap(fromElement,
//					inclusive));
			
		}

		public NavigableSet<E> subSet(E fromElement, E toElement) {
			return subSet(fromElement, true, toElement, false);
		}

		public NavigableSet<E> headSet(E toElement) {
			return headSet(toElement, false);
		}

		public NavigableSet<E> tailSet(E fromElement) {
			return tailSet(fromElement, true);
		}

		public NavigableSet<E> descendingSet() {
			//TODO this is not implemented
			return null;
//			return new ConcurrentSkipListSet(m.descendingMap());
		}
	}

	static final class Values<E> extends AbstractCollection<E> {
		private final ConcurrentNavigableMap<Object, E> m;

		Values(ConcurrentNavigableMap<Object, E> map) {
			m = map;
		}

		public Iterator<E> iterator() {
			if (m instanceof NonBlockingJavaSkipListMap)
				return ((NonBlockingJavaSkipListMap<Object, E>) m)
						.valueIterator();
			else
				return ((SubMap<Object, E>) m).valueIterator();
		}

		public boolean isEmpty() {
			return m.isEmpty();
		}

		public int size() {
			return m.size();
		}

		public boolean contains(Object o) {
			return m.containsValue(o);
		}

		public void clear() {
			m.clear();
		}

		public Object[] toArray() {
			return toList(this).toArray();
		}

		public <T> T[] toArray(T[] a) {
			return toList(this).toArray(a);
		}
	}

	static final class EntrySet<K1, V1> extends AbstractSet<Map.Entry<K1, V1>> {
		private final ConcurrentNavigableMap<K1, V1> m;

		EntrySet(ConcurrentNavigableMap<K1, V1> map) {
			m = map;
		}

		public Iterator<Map.Entry<K1, V1>> iterator() {
			if (m instanceof NonBlockingJavaSkipListMap)
				return ((NonBlockingJavaSkipListMap<K1, V1>) m).entryIterator();
			else
				return ((SubMap<K1, V1>) m).entryIterator();
		}

		public boolean contains(Object o) {
			if (!(o instanceof Map.Entry))
				return false;
			Map.Entry<K1, V1> e = (Map.Entry<K1, V1>) o;
			V1 v = m.get(e.getKey());
			return v != null && v.equals(e.getValue());
		}

		public boolean remove(Object o) {
			if (!(o instanceof Map.Entry))
				return false;
			Map.Entry<K1, V1> e = (Map.Entry<K1, V1>) o;
			return m.remove(e.getKey(), e.getValue());
		}

		public boolean isEmpty() {
			return m.isEmpty();
		}

		public int size() {
			return m.size();
		}

		public void clear() {
			m.clear();
		}

		public boolean equals(Object o) {
			if (o == this)
				return true;
			if (!(o instanceof Set))
				return false;
			Collection<?> c = (Collection<?>) o;
			try {
				return containsAll(c) && c.containsAll(this);
			} catch (ClassCastException unused) {
				return false;
			} catch (NullPointerException unused) {
				return false;
			}
		}

		public Object[] toArray() {
			return toList(this).toArray();
		}

		public <T> T[] toArray(T[] a) {
			return toList(this).toArray(a);
		}
	}

	/**
	 * Submaps returned by {@link NonBlockingJavaSkipListMap} submap operations
	 * represent a subrange of mappings of their underlying maps. Instances of
	 * this class support all methods of their underlying maps, differing in
	 * that mappings outside their range are ignored, and attempts to add
	 * mappings outside their ranges result in {@link IllegalArgumentException}.
	 * Instances of this class are constructed only using the <tt>subMap</tt>,
	 * <tt>headMap</tt>, and <tt>tailMap</tt> methods of their underlying maps.
	 * 
	 * @serial include
	 */
	static final class SubMap<K, V> extends AbstractMap<K, V> implements
			ConcurrentNavigableMap<K, V>, Cloneable, java.io.Serializable {
		private static final long serialVersionUID = -7647078645895051609L;

		/** Underlying map */
		private final NonBlockingJavaSkipListMap<K, V> m;
		/** lower bound key, or null if from start */
		private final K lo;
		/** upper bound key, or null if to end */
		private final K hi;
		/** inclusion flag for lo */
		private final boolean loInclusive;
		/** inclusion flag for hi */
		private final boolean hiInclusive;
		/** direction */
		private final boolean isDescending;

		// Lazily initialized view holders
		private transient KeySet<K> keySetView;
		private transient Set<Map.Entry<K, V>> entrySetView;
		private transient Collection<V> valuesView;

		/**
		 * Creates a new submap, initializing all fields
		 */
		SubMap(NonBlockingJavaSkipListMap<K, V> map, K fromKey,
				boolean fromInclusive, K toKey, boolean toInclusive,
				boolean isDescending) {
			if (fromKey != null && toKey != null
					&& map.compare(fromKey, toKey) > 0)
				throw new IllegalArgumentException("inconsistent range");
			this.m = map;
			this.lo = fromKey;
			this.hi = toKey;
			this.loInclusive = fromInclusive;
			this.hiInclusive = toInclusive;
			this.isDescending = isDescending;
		}

		/* ---------------- Utilities -------------- */

		private boolean tooLow(K key) {
			if (lo != null) {
				int c = m.compare(key, lo);
				if (c < 0 || (c == 0 && !loInclusive))
					return true;
			}
			return false;
		}

		private boolean tooHigh(K key) {
			if (hi != null) {
				int c = m.compare(key, hi);
				if (c > 0 || (c == 0 && !hiInclusive))
					return true;
			}
			return false;
		}

		private boolean inBounds(K key) {
			return !tooLow(key) && !tooHigh(key);
		}

		private void checkKeyBounds(K key) throws IllegalArgumentException {
			if (key == null)
				throw new NullPointerException();
			if (!inBounds(key))
				throw new IllegalArgumentException("key out of range");
		}

		/**
		 * Returns true if node key is less than upper bound of range
		 */
		private boolean isBeforeEnd(NonBlockingJavaSkipListMap.Node<K, V> n) {
			if (n == null)
				return false;
			if (hi == null)
				return true;
			K k = n.key;
			if (k == null) // pass by markers and headers
				return true;
			int c = m.compare(k, hi);
			if (c > 0 || (c == 0 && !hiInclusive))
				return false;
			return true;
		}

		/**
		 * Returns lowest node. This node might not be in range, so most usages
		 * need to check bounds
		 */
		private NonBlockingJavaSkipListMap.Node<K, V> loNode() {
			if (lo == null)
				return m.findFirst();
			else if (loInclusive)
				return m.findNear(lo, m.GT | m.EQ);
			else
				return m.findNear(lo, m.GT);
		}

		/**
		 * Returns highest node. This node might not be in range, so most usages
		 * need to check bounds
		 */
		private NonBlockingJavaSkipListMap.Node<K, V> hiNode() {
			if (hi == null)
				return m.findLast();
			else if (hiInclusive)
				return m.findNear(hi, m.LT | m.EQ);
			else
				return m.findNear(hi, m.LT);
		}

		/**
		 * Returns lowest absolute key (ignoring directonality)
		 */
		private K lowestKey() {
			NonBlockingJavaSkipListMap.Node<K, V> n = loNode();
			if (isBeforeEnd(n))
				return n.key;
			else
				throw new NoSuchElementException();
		}

		/**
		 * Returns highest absolute key (ignoring directonality)
		 */
		private K highestKey() {
			NonBlockingJavaSkipListMap.Node<K, V> n = hiNode();
			if (n != null) {
				K last = n.key;
				if (inBounds(last))
					return last;
			}
			throw new NoSuchElementException();
		}

		private Map.Entry<K, V> lowestEntry() {
			for (;;) {
				NonBlockingJavaSkipListMap.Node<K, V> n = loNode();
				if (!isBeforeEnd(n))
					return null;
				Map.Entry<K, V> e = n.createSnapshot();
				if (e != null)
					return e;
			}
		}

		private Map.Entry<K, V> highestEntry() {
			for (;;) {
				NonBlockingJavaSkipListMap.Node<K, V> n = hiNode();
				if (n == null || !inBounds(n.key))
					return null;
				Map.Entry<K, V> e = n.createSnapshot();
				if (e != null)
					return e;
			}
		}

		private Map.Entry<K, V> removeLowest() {
			for (;;) {
				Node<K, V> n = loNode();
				if (n == null)
					return null;
				K k = n.key;
				if (!inBounds(k))
					return null;
				V v = m.doRemove(k, null);
				if (v != null)
					return new AbstractMap.SimpleImmutableEntry<K, V>(k, v);
			}
		}

		private Map.Entry<K, V> removeHighest() {
			for (;;) {
				Node<K, V> n = hiNode();
				if (n == null)
					return null;
				K k = n.key;
				if (!inBounds(k))
					return null;
				V v = m.doRemove(k, null);
				if (v != null)
					return new AbstractMap.SimpleImmutableEntry<K, V>(k, v);
			}
		}

		/**
		 * Submap version of ConcurrentSkipListMap.getNearEntry
		 */
		private Map.Entry<K, V> getNearEntry(K key, int rel) {
			if (isDescending) { // adjust relation for direction
				if ((rel & m.LT) == 0)
					rel |= m.LT;
				else
					rel &= ~m.LT;
			}
			if (tooLow(key))
				return ((rel & m.LT) != 0) ? null : lowestEntry();
			if (tooHigh(key))
				return ((rel & m.LT) != 0) ? highestEntry() : null;
			for (;;) {
				Node<K, V> n = m.findNear(key, rel);
				if (n == null || !inBounds(n.key))
					return null;
				K k = n.key;
				V v = n.getValidValue();
				if (v != null)
					return new AbstractMap.SimpleImmutableEntry<K, V>(k, v);
			}
		}

		// Almost the same as getNearEntry, except for keys
		private K getNearKey(K key, int rel) {
			if (isDescending) { // adjust relation for direction
				if ((rel & m.LT) == 0)
					rel |= m.LT;
				else
					rel &= ~m.LT;
			}
			if (tooLow(key)) {
				if ((rel & m.LT) == 0) {
					NonBlockingJavaSkipListMap.Node<K, V> n = loNode();
					if (isBeforeEnd(n))
						return n.key;
				}
				return null;
			}
			if (tooHigh(key)) {
				if ((rel & m.LT) != 0) {
					NonBlockingJavaSkipListMap.Node<K, V> n = hiNode();
					if (n != null) {
						K last = n.key;
						if (inBounds(last))
							return last;
					}
				}
				return null;
			}
			for (;;) {
				Node<K, V> n = m.findNear(key, rel);
				if (n == null || !inBounds(n.key))
					return null;
				K k = n.key;
				V v = n.getValidValue();
				if (v != null)
					return k;
			}
		}

		/* ---------------- Map API methods -------------- */

		public boolean containsKey(Object key) {
			if (key == null)
				throw new NullPointerException();
			K k = (K) key;
			return inBounds(k) && m.containsKey(k);
		}

		public V get(Object key) {
			if (key == null)
				throw new NullPointerException();
			K k = (K) key;
			return ((!inBounds(k)) ? null : m.get(k));
		}

		public V put(K key, V value) {
			checkKeyBounds(key);
			return m.put(key, value);
		}

		public V remove(Object key) {
			K k = (K) key;
			return (!inBounds(k)) ? null : m.remove(k);
		}

		public int size() {
			long count = 0;
			for (NonBlockingJavaSkipListMap.Node<K, V> n = loNode(); isBeforeEnd(n); n = n.next) {
				if (n.getValidValue() != null)
					++count;
			}
			return count >= Integer.MAX_VALUE ? Integer.MAX_VALUE : (int) count;
		}

		public boolean isEmpty() {
			return !isBeforeEnd(loNode());
		}

		public boolean containsValue(Object value) {
			if (value == null)
				throw new NullPointerException();
			for (NonBlockingJavaSkipListMap.Node<K, V> n = loNode(); isBeforeEnd(n); n = n.next) {
				V v = n.getValidValue();
				if (v != null && value.equals(v))
					return true;
			}
			return false;
		}

		public void clear() {
			for (NonBlockingJavaSkipListMap.Node<K, V> n = loNode(); isBeforeEnd(n); n = n.next) {
				if (n.getValidValue() != null)
					m.remove(n.key);
			}
		}

		/* ---------------- ConcurrentMap API methods -------------- */

		public V putIfAbsent(K key, V value) {
			checkKeyBounds(key);
			return m.putIfAbsent(key, value);
		}

		public boolean remove(Object key, Object value) {
			K k = (K) key;
			return inBounds(k) && m.remove(k, value);
		}

		public boolean replace(K key, V oldValue, V newValue) {
			checkKeyBounds(key);
			return m.replace(key, oldValue, newValue);
		}

		public V replace(K key, V value) {
			checkKeyBounds(key);
			return m.replace(key, value);
		}

		/* ---------------- SortedMap API methods -------------- */

		public Comparator<? super K> comparator() {
			Comparator<? super K> cmp = m.comparator();
			if (isDescending)
				return Collections.reverseOrder(cmp);
			else
				return cmp;
		}

		/**
		 * Utility to create submaps, where given bounds override
		 * unbounded(null) ones and/or are checked against bounded ones.
		 */
		private SubMap<K, V> newSubMap(K fromKey, boolean fromInclusive,
				K toKey, boolean toInclusive) {
			if (isDescending) { // flip senses
				K tk = fromKey;
				fromKey = toKey;
				toKey = tk;
				boolean ti = fromInclusive;
				fromInclusive = toInclusive;
				toInclusive = ti;
			}
			if (lo != null) {
				if (fromKey == null) {
					fromKey = lo;
					fromInclusive = loInclusive;
				} else {
					int c = m.compare(fromKey, lo);
					if (c < 0 || (c == 0 && !loInclusive && fromInclusive))
						throw new IllegalArgumentException("key out of range");
				}
			}
			if (hi != null) {
				if (toKey == null) {
					toKey = hi;
					toInclusive = hiInclusive;
				} else {
					int c = m.compare(toKey, hi);
					if (c > 0 || (c == 0 && !hiInclusive && toInclusive))
						throw new IllegalArgumentException("key out of range");
				}
			}
			return new SubMap<K, V>(m, fromKey, fromInclusive, toKey,
					toInclusive, isDescending);
		}

		public SubMap<K, V> subMap(K fromKey, boolean fromInclusive, K toKey,
				boolean toInclusive) {
			if (fromKey == null || toKey == null)
				throw new NullPointerException();
			return newSubMap(fromKey, fromInclusive, toKey, toInclusive);
		}

		public SubMap<K, V> headMap(K toKey, boolean inclusive) {
			if (toKey == null)
				throw new NullPointerException();
			return newSubMap(null, false, toKey, inclusive);
		}

		public SubMap<K, V> tailMap(K fromKey, boolean inclusive) {
			if (fromKey == null)
				throw new NullPointerException();
			return newSubMap(fromKey, inclusive, null, false);
		}

		public SubMap<K, V> subMap(K fromKey, K toKey) {
			return subMap(fromKey, true, toKey, false);
		}

		public SubMap<K, V> headMap(K toKey) {
			return headMap(toKey, false);
		}

		public SubMap<K, V> tailMap(K fromKey) {
			return tailMap(fromKey, true);
		}

		public SubMap<K, V> descendingMap() {
			return new SubMap<K, V>(m, lo, loInclusive, hi, hiInclusive,
					!isDescending);
		}

		/* ---------------- Relational methods -------------- */

		public Map.Entry<K, V> ceilingEntry(K key) {
			return getNearEntry(key, (m.GT | m.EQ));
		}

		public K ceilingKey(K key) {
			return getNearKey(key, (m.GT | m.EQ));
		}

		public Map.Entry<K, V> lowerEntry(K key) {
			return getNearEntry(key, (m.LT));
		}

		public K lowerKey(K key) {
			return getNearKey(key, (m.LT));
		}

		public Map.Entry<K, V> floorEntry(K key) {
			return getNearEntry(key, (m.LT | m.EQ));
		}

		public K floorKey(K key) {
			return getNearKey(key, (m.LT | m.EQ));
		}

		public Map.Entry<K, V> higherEntry(K key) {
			return getNearEntry(key, (m.GT));
		}

		public K higherKey(K key) {
			return getNearKey(key, (m.GT));
		}

		public K firstKey() {
			return isDescending ? highestKey() : lowestKey();
		}

		public K lastKey() {
			return isDescending ? lowestKey() : highestKey();
		}

		public Map.Entry<K, V> firstEntry() {
			return isDescending ? highestEntry() : lowestEntry();
		}

		public Map.Entry<K, V> lastEntry() {
			return isDescending ? lowestEntry() : highestEntry();
		}

		public Map.Entry<K, V> pollFirstEntry() {
			return isDescending ? removeHighest() : removeLowest();
		}

		public Map.Entry<K, V> pollLastEntry() {
			return isDescending ? removeLowest() : removeHighest();
		}

		/* ---------------- Submap Views -------------- */

		public NavigableSet<K> keySet() {
			KeySet<K> ks = keySetView;
			return (ks != null) ? ks : (keySetView = new KeySet(this));
		}

		public NavigableSet<K> navigableKeySet() {
			KeySet<K> ks = keySetView;
			return (ks != null) ? ks : (keySetView = new KeySet(this));
		}

		public Collection<V> values() {
			Collection<V> vs = valuesView;
			return (vs != null) ? vs : (valuesView = new Values(this));
		}

		public Set<Map.Entry<K, V>> entrySet() {
			Set<Map.Entry<K, V>> es = entrySetView;
			return (es != null) ? es : (entrySetView = new EntrySet(this));
		}

		public NavigableSet<K> descendingKeySet() {
			return descendingMap().navigableKeySet();
		}

		Iterator<K> keyIterator() {
			return new SubMapKeyIterator();
		}

		Iterator<V> valueIterator() {
			return new SubMapValueIterator();
		}

		Iterator<Map.Entry<K, V>> entryIterator() {
			return new SubMapEntryIterator();
		}

		/**
		 * Variant of main Iter class to traverse through submaps.
		 */
		abstract class SubMapIter<T> implements Iterator<T> {
			/** the last node returned by next() */
			Node<K, V> lastReturned;
			/** the next node to return from next(); */
			Node<K, V> next;
			/** Cache of next value field to maintain weak consistency */
			V nextValue;

			SubMapIter() {
				for (;;) {
					next = isDescending ? hiNode() : loNode();
					if (next == null)
						break;
					Object x = next.value;
					if (x != null && x != next) {
						if (!inBounds(next.key))
							next = null;
						else
							nextValue = (V) x;
						break;
					}
				}
			}

			public final boolean hasNext() {
				return next != null;
			}

			final void advance() {
				if (next == null)
					throw new NoSuchElementException();
				lastReturned = next;
				if (isDescending)
					descend();
				else
					ascend();
			}

			private void ascend() {
				for (;;) {
					next = next.next;
					if (next == null)
						break;
					Object x = next.value;
					if (x != null && x != next) {
						if (tooHigh(next.key))
							next = null;
						else
							nextValue = (V) x;
						break;
					}
				}
			}

			private void descend() {
				for (;;) {
					next = m.findNear(lastReturned.key, LT);
					if (next == null)
						break;
					Object x = next.value;
					if (x != null && x != next) {
						if (tooLow(next.key))
							next = null;
						else
							nextValue = (V) x;
						break;
					}
				}
			}

			public void remove() {
				Node<K, V> l = lastReturned;
				if (l == null)
					throw new IllegalStateException();
				m.remove(l.key);
				lastReturned = null;
			}

		}

		final class SubMapValueIterator extends SubMapIter<V> {
			public V next() {
				V v = nextValue;
				advance();
				return v;
			}
		}

		final class SubMapKeyIterator extends SubMapIter<K> {
			public K next() {
				Node<K, V> n = next;
				advance();
				return n.key;
			}
		}

		final class SubMapEntryIterator extends SubMapIter<Map.Entry<K, V>> {
			public Map.Entry<K, V> next() {
				Node<K, V> n = next;
				V v = nextValue;
				advance();
				return new AbstractMap.SimpleImmutableEntry<K, V>(n.key, v);
			}
		}
	}
}
